Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.aawt)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-17/4, b>=a

For fixed z and a=-17/4, b=5

http://functions.wolfram.com/07.23.03.aawt.01

Input Form

Hypergeometric2F1[-(17/4), 5, 19/4, z] == (1/(34359738368 z^(15/4))) (11 (2 z^(3/4) (-255255 - 1037595 z - 4644315 z^2 + 1523512193 z^3 - 6234661685 z^4 + 9581692575 z^5 - 6530931225 z^6 + 1665538875 z^7) + 69615 (-1 + z)^4 (-11 - 84 z - 450 z^2 - 2900 z^3 + 23925 z^4) ArcTan[z^(1/4)] - 69615 (-1 + z)^4 (-11 - 84 z - 450 z^2 - 2900 z^3 + 23925 z^4) ArcTanh[z^(1/4)]))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]